Olena O. Bulatsyk

Comparing different approaches to linear antenna synthesis problems according to power radiation pattern

The antenna synthesis problem according to the prescribed power radiation pattern with the equality norm condition is solved by the approach based on the concept of generating polynomials. The variational formulation, supplied by the Lagrange method of multipliers, is applied. The modified Newton method is used for numerical solving of the respective integro-transcendental equation systems. The approach was numerically tested on the example of the antenna synthesis problem, recently solved directly by the Newton method. Numerical results are compared and analyzed.

Structure of phase-asymmetric solutions of circular antenna synthesis problem by amplitude radiation pattern with axially independent data

The synthesis problem by the amplitude radiation pattern is considered for the circular aperture antennas. The prescribed pattern is assumed to be axially-symmetric. The solutions with asymmetric phase patterns are analyzed numerically.

Synthesis of circular aperture antenna by amplitude radiation pattern of Fourier harmonics

The synthesis problem by the amplitude radiation pattern is considered for the circular aperture antennas. The conception of circular harmonics is used. The representation by generating polynomials is used for each harmonic separately. The numerical results are presented for the harmonic of the first order (infundibular pattern).

Polynomial approach to linear antenna array synthesis problem according to power radiation pattern with restriction on its norm

The synthesis problem for equidistant linear antenna array according to the prescribed power radiation pattern (RP) is generalized by taking into account an additional restriction on the norm of the synthesized RP. The variational approach supplemented by the Lagrange method of multipliers is applied for the formulation of problem. The phase RP is uniquely represented by the complex polynomial of high degree. The modified Newton method is used for numerical solving the respective integral-transcendental equation system. The approach was numerically applied to an example of the antenna array synthesis problem.

Complex zeros of solutions to the synthesis problem of irregular linear antenna array by amplitude radiation pattern

The synthesis problem for nonuniformly spaced linear antenna arrays by the amplitude radiation pattern is considered. Distribution of complex zeros of its solutions is numerically analyzed. Results partially confirm the hypothesis that these zeros describe the minimal complex factor of the solutions. Distribution of complex zeros of its solutions is numerically analyzed. Results partially confirm the hypothesis that these zeros describe the minimal complex factor of the solutions.

Generalization of an integro-transcendetnal equation system with vanishing solutions in free phase problem

The nonlinear integral equation of Hammerstein type with the linear dependence of the argument of unknown function and nonlinear dependency on its modulus is considered. Solutions of this equation are represented by means of polynomials of finite degree describing, in particular, zeros of these solutions. For the case of solutions vanishing in the considered interval, new system of integro-transcendental equation is obtained.

Generalized nonlinear integral equation of hammerstein type

A nonlinear integral equation generalizing that arisen in the antenna synthesis problems is investigated. The semi-analytical solutions are found. They parameters are determined from an equation system consisting of a linearized integral equation and finite-dimensional system of transcendental ones. Branching of the solution is investigated. A particular case related to Fourier transform is numerically analyzed.

Application of modified Newton method to nonlinear integral equation of circular antenna synthesis problem

An equation arisen in the synthesis problem of antenna systems according to the prescribed amplitude radiation pattern is investigated. The proposed modification of the Newton method allows finding the branched solutions depending on the value of characteristic physical parameter. The algorithm is described and numerical results are presented.